Eigenvalues of the Laplace-Beltrami operator on a prolate spheroid

被引：1

作者：

Volkmer, Hans ^{[1
]}

机构：

[1] Univ Wisconsin Milwaukee, Dept Math Sci, Milwaukee, WI 53211 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 373卷

关键词：

Laplace-Beltrami operator; Prolate spheroid; Singular Sturm-Liouville problem; Generalized matrix eigenvalue problem;

D O I：

10.1016/j.jde.2023.07.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Laplace-Beltrami operator on a prolate spheroid admits a sequence of eigenvalues. These eigenvalues are determined by a singular Sturm-Liouville problem. Properties of the eigenvalues are obtained using the minimum-maximum principle and the Prefer angle. In particular, eigenvalues are approximated by those of generalized matrix eigenvalue problems, and their behavior is studied when the eccentricity of the spheroid approaches 0 or 1.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：411 / 445

页数：35

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